b. Comparative advantage goes to the low opportunity cost producer.
The opportunity cost of corn in the US is 2/5 melon. To produce a bushel of
corn, we require 1/5 of a unit of labor, and 1/5 of a unit of labor could
have produced 2/5 melon.
You should be able to show that the opportunity cost of a melon in the US is 5/2 bushel of corn.
In Mexico, the opportunity cost of corn is 1 melon -- and the opportunity cost of a melon is 1 bushel of corn. One worker could have produced either good.
The US is therefore the low opportunity cost producer of corn (2/5 < 1) and Mexico the low opportunity cost producer of melons (1 < 5/2)
c. Price ratios after trade must lie between the Mexican and US pre-trade price ratios or relative prices. In Mexico before trade, 1 worker could produce either 1 bushel of corn or one melon; the Mexican price ratio would therefore be Px/Py = 1.
In the US, the activity requirement for corn was 1/5; the price of corn would therefore have been (at a minimum) (1/5) w. The activity requirement for melons is 1/2, so the US price of melons would have been (1/2) w (at a minimum). The US price ratio is therefore
Prices reflect opportunity costs in both the US and Mexico. The price ratio after trade must therefore lie between 2/5 and 1.
We assume a price ratio of 2/3, which does lie between 2/5 and 1.
To draw the PPF, we must calculate the maximum possible production of corn and melons in the US and in Mexico.
| Country | Corn | Melons |
|---|---|---|
| United States | 5000 | 2000 |
| Mexico | 1000 | 1000 |
Note: you might be worried that this is beyond Mexican production possibilities, too. If the US actually tried to buy more melons than Mexico produced, the price of Mexican melons would rise. The difficulty here comes because we are simply assuming an international price for melons which might not be sustainable in the market. But before we can deal with the difficulty, we will have to turn to the study of how markets operate.
Each Mexican melon would buy 3/2 of a bushel of corn. The whole 1000 Mexican melons would therefore buy 1,500 bushels of corn -- beyond Mexican production possibilities.
Remember that Mexico was at an absolute disadvantage in the production of both goods. Nevertheless, her Trading Possibility Frontier does indicate that Mexico has more choices after trade than before trade.